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Gov. Cuomo’s plan to provide free tuition to low- and middle-income students at CUNY and SUNY public colleges will cripple enrollment at many private colleges, officials at those schools fear.

Many of the 100-plus nonprofit and for-profit colleges in New York compete with public colleges for the same students.

Smaller private schools are particularly vulnerable.

“It could change the balance of students attending public colleges and private colleges. It could potentially impact enrollment,” said Kevin Cavanagh, executive vice president of strategic planning at the College of New Rochelle.

It’s a double whammy for CNR, which was already grappling with fiscal woes before Cuomo’s free-tuition announcement.

“We’ve been already competing with those colleges on costs. Families are making their decision on the bottom line and value,” Cavanagh said.

Higher-ed sources say the more selective, top-tier private institutions that enroll students from across the country — such as Columbia, Cornell, NYU and Cuomo’s alma mater, Fordham — would not be affected.

With Bernie Sanders at his side, Cuomo last week unveiled a plan that would provide any full-time student with family income up to $125,000 free tuition at City University or State University campuses.

But New York also has a $1 billion Tuition Assistance Program that provides financial grants to students who attend public or private colleges.

Private-college officials said Cuomo and the state Legislature should address the issue more broadly — increasing tuition aid for all students, regardless of where they go to school.

“When it comes to financial aid, the state policy has always been about treating all students the same. It’s been a great public-private partnership. This proposal tears away that,” said Mary Beth Labate, president of the Commission on Independent Colleges and Universities (CICU), and Cuomo’s former budget director.